843 lines
37 KiB
Plaintext
843 lines
37 KiB
Plaintext
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FFTW FREQUENTLY ASKED QUESTIONS WITH ANSWERS
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14 Sep 2021
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Matteo Frigo
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Steven G. Johnson
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<fftw@fftw.org>
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This is the list of Frequently Asked Questions about FFTW, a collection of
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fast C routines for computing the Discrete Fourier Transform in one or
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more dimensions.
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===============================================================================
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Index
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Section 1. Introduction and General Information
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Q1.1 What is FFTW?
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Q1.2 How do I obtain FFTW?
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Q1.3 Is FFTW free software?
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Q1.4 What is this about non-free licenses?
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Q1.5 In the West? I thought MIT was in the East?
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Section 2. Installing FFTW
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Q2.1 Which systems does FFTW run on?
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Q2.2 Does FFTW run on Windows?
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Q2.3 My compiler has trouble with FFTW.
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Q2.4 FFTW does not compile on Solaris, complaining about const.
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Q2.5 What's the difference between --enable-3dnow and --enable-k7?
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Q2.6 What's the difference between the fma and the non-fma versions?
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Q2.7 Which language is FFTW written in?
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Q2.8 Can I call FFTW from Fortran?
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Q2.9 Can I call FFTW from C++?
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Q2.10 Why isn't FFTW written in Fortran/C++?
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Q2.11 How do I compile FFTW to run in single precision?
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Q2.12 --enable-k7 does not work on x86-64
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Section 3. Using FFTW
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Q3.1 Why not support the FFTW 2 interface in FFTW 3?
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Q3.2 Why do FFTW 3 plans encapsulate the input/output arrays and not ju
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Q3.3 FFTW seems really slow.
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Q3.4 FFTW slows down after repeated calls.
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Q3.5 An FFTW routine is crashing when I call it.
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Q3.6 My Fortran program crashes when calling FFTW.
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Q3.7 FFTW gives results different from my old FFT.
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Q3.8 FFTW gives different results between runs
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Q3.9 Can I save FFTW's plans?
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Q3.10 Why does your inverse transform return a scaled result?
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Q3.11 How can I make FFTW put the origin (zero frequency) at the center
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Q3.12 How do I FFT an image/audio file in *foobar* format?
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Q3.13 My program does not link (on Unix).
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Q3.14 I included your header, but linking still fails.
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Q3.15 My program crashes, complaining about stack space.
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Q3.16 FFTW seems to have a memory leak.
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Q3.17 The output of FFTW's transform is all zeros.
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Q3.18 How do I call FFTW from the Microsoft language du jour?
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Q3.19 Can I compute only a subset of the DFT outputs?
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Q3.20 Can I use FFTW's routines for in-place and out-of-place matrix tra
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Section 4. Internals of FFTW
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Q4.1 How does FFTW work?
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Q4.2 Why is FFTW so fast?
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Section 5. Known bugs
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Q5.1 FFTW 1.1 crashes in rfftwnd on Linux.
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Q5.2 The MPI transforms in FFTW 1.2 give incorrect results/leak memory.
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Q5.3 The test programs in FFTW 1.2.1 fail when I change FFTW to use sin
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Q5.4 The test program in FFTW 1.2.1 fails for n > 46340.
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Q5.5 The threaded code fails on Linux Redhat 5.0
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Q5.6 FFTW 2.0's rfftwnd fails for rank > 1 transforms with a final dime
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Q5.7 FFTW 2.0's complex transforms give the wrong results with prime fa
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Q5.8 FFTW 2.1.1's MPI test programs crash with MPICH.
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Q5.9 FFTW 2.1.2's multi-threaded transforms don't work on AIX.
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Q5.10 FFTW 2.1.2's complex transforms give incorrect results for large p
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Q5.11 FFTW 2.1.3's multi-threaded transforms don't give any speedup on S
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Q5.12 FFTW 2.1.3 crashes on AIX.
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===============================================================================
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Section 1. Introduction and General Information
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Q1.1 What is FFTW?
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Q1.2 How do I obtain FFTW?
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Q1.3 Is FFTW free software?
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Q1.4 What is this about non-free licenses?
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Q1.5 In the West? I thought MIT was in the East?
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-------------------------------------------------------------------------------
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Question 1.1. What is FFTW?
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FFTW is a free collection of fast C routines for computing the Discrete
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Fourier Transform in one or more dimensions. It includes complex, real,
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symmetric, and parallel transforms, and can handle arbitrary array sizes
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efficiently. FFTW is typically faster than other publically-available FFT
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implementations, and is even competitive with vendor-tuned libraries.
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(See our web page for extensive benchmarks.) To achieve this performance,
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FFTW uses novel code-generation and runtime self-optimization techniques
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(along with many other tricks).
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-------------------------------------------------------------------------------
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Question 1.2. How do I obtain FFTW?
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FFTW can be found at the FFTW web page. You can also retrieve it from
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ftp.fftw.org in /pub/fftw.
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-------------------------------------------------------------------------------
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Question 1.3. Is FFTW free software?
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Starting with version 1.3, FFTW is Free Software in the technical sense
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defined by the Free Software Foundation (see Categories of Free and
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Non-Free Software), and is distributed under the terms of the GNU General
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Public License. Previous versions of FFTW were distributed without fee
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for noncommercial use, but were not technically ``free.''
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Non-free licenses for FFTW are also available that permit different terms
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of use than the GPL.
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-------------------------------------------------------------------------------
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Question 1.4. What is this about non-free licenses?
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The non-free licenses are for companies that wish to use FFTW in their
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products but are unwilling to release their software under the GPL (which
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would require them to release source code and allow free redistribution).
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Such users can purchase an unlimited-use license from MIT. Contact us for
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more details.
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We could instead have released FFTW under the LGPL, or even disallowed
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non-Free usage. Suffice it to say, however, that MIT owns the copyright
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to FFTW and they only let us GPL it because we convinced them that it
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would neither affect their licensing revenue nor irritate existing
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licensees.
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-------------------------------------------------------------------------------
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Question 1.5. In the West? I thought MIT was in the East?
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Not to an Italian. You could say that we're a Spaghetti Western (with
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apologies to Sergio Leone).
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===============================================================================
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Section 2. Installing FFTW
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Q2.1 Which systems does FFTW run on?
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Q2.2 Does FFTW run on Windows?
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Q2.3 My compiler has trouble with FFTW.
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Q2.4 FFTW does not compile on Solaris, complaining about const.
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Q2.5 What's the difference between --enable-3dnow and --enable-k7?
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Q2.6 What's the difference between the fma and the non-fma versions?
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Q2.7 Which language is FFTW written in?
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Q2.8 Can I call FFTW from Fortran?
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Q2.9 Can I call FFTW from C++?
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Q2.10 Why isn't FFTW written in Fortran/C++?
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Q2.11 How do I compile FFTW to run in single precision?
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Q2.12 --enable-k7 does not work on x86-64
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-------------------------------------------------------------------------------
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Question 2.1. Which systems does FFTW run on?
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FFTW is written in ANSI C, and should work on any system with a decent C
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compiler. (See also Q2.2 `Does FFTW run on Windows?', Q2.3 `My compiler
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has trouble with FFTW.'.) FFTW can also take advantage of certain
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hardware-specific features, such as cycle counters and SIMD instructions,
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but this is optional.
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-------------------------------------------------------------------------------
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Question 2.2. Does FFTW run on Windows?
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Yes, many people have reported successfully using FFTW on Windows with
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various compilers. FFTW was not developed on Windows, but the source code
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is essentially straight ANSI C. See also the FFTW Windows installation
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notes, Q2.3 `My compiler has trouble with FFTW.', and Q3.18 `How do I call
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FFTW from the Microsoft language du jour?'.
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-------------------------------------------------------------------------------
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Question 2.3. My compiler has trouble with FFTW.
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Complain fiercely to the vendor of the compiler.
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We have successfully used gcc 3.2.x on x86 and PPC, a recent Compaq C
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compiler for Alpha, version 6 of IBM's xlc compiler for AIX, Intel's icc
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versions 5-7, and Sun WorkShop cc version 6.
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FFTW is likely to push compilers to their limits, however, and several
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compiler bugs have been exposed by FFTW. A partial list follows.
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gcc 2.95.x for Solaris/SPARC produces incorrect code for the test program
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(workaround: recompile the libbench2 directory with -O2).
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NetBSD/macppc 1.6 comes with a gcc version that also miscompiles the test
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program. (Please report a workaround if you know one.)
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gcc 3.2.3 for ARM reportedly crashes during compilation. This bug is
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reportedly fixed in later versions of gcc.
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Versions 8.0 and 8.1 of Intel's icc falsely claim to be gcc, so you should
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specify CC="icc -no-gcc"; this is automatic in FFTW 3.1. icc-8.0.066
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reportely produces incorrect code for FFTW 2.1.5, but is fixed in version
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8.1. icc-7.1 compiler build 20030402Z appears to produce incorrect
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dependencies, causing the compilation to fail. icc-7.1 build 20030307Z
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appears to work fine. (Use icc -V to check which build you have.) As of
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2003/04/18, build 20030402Z appears not to be available any longer on
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Intel's website, whereas the older build 20030307Z is available.
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ranlib of GNU binutils 2.9.1 on Irix has been observed to corrupt the FFTW
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libraries, causing a link failure when FFTW is compiled. Since ranlib is
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completely superfluous on Irix, we suggest deleting it from your system
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and replacing it with a symbolic link to /bin/echo.
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If support for SIMD instructions is enabled in FFTW, further compiler
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problems may appear:
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gcc 3.4.[0123] for x86 produces incorrect SSE2 code for FFTW when -O2 (the
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best choice for FFTW) is used, causing FFTW to crash (make check crashes).
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This bug is fixed in gcc 3.4.4. On x86_64 (amd64/em64t), gcc 3.4.4
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reportedly still has a similar problem, but this is fixed as of gcc 3.4.6.
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gcc-3.2 for x86 produces incorrect SIMD code if -O3 is used. The same
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compiler produces incorrect SIMD code if no optimization is used, too.
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When using gcc-3.2, it is a good idea not to change the default CFLAGS
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selected by the configure script.
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Some 3.0.x and 3.1.x versions of gcc on x86 may crash. gcc so-called 2.96
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shipping with RedHat 7.3 crashes when compiling SIMD code. In both cases,
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please upgrade to gcc-3.2 or later.
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Intel's icc 6.0 misaligns SSE constants, but FFTW has a workaround. icc
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8.x fails to compile FFTW 3.0.x because it falsely claims to be gcc; we
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believe this to be a bug in icc, but FFTW 3.1 has a workaround.
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Visual C++ 2003 reportedly produces incorrect code for SSE/SSE2 when
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compiling FFTW. This bug was reportedly fixed in VC++ 2005;
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alternatively, you could switch to the Intel compiler. VC++ 6.0 also
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reportedly produces incorrect code for the file reodft11e-r2hc-odd.c
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unless optimizations are disabled for that file.
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gcc 2.95 on MacOS X miscompiles AltiVec code (fixed in later versions).
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gcc 3.2.x miscompiles AltiVec permutations, but FFTW has a workaround.
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gcc 4.0.1 on MacOS for Intel crashes when compiling FFTW; a workaround is
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to compile one file without optimization: cd kernel; make CFLAGS=" "
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trig.lo.
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gcc 4.1.1 reportedly crashes when compiling FFTW for MIPS; the workaround
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is to compile the file it crashes on (t2_64.c) with a lower optimization
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level.
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gcc versions 4.1.2 to 4.2.0 for x86 reportedly miscompile FFTW 3.1's test
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program, causing make check to crash (gcc bug #26528). The bug was
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reportedly fixed in gcc version 4.2.1 and later. A workaround is to
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compile libbench2/verify-lib.c without optimization.
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-------------------------------------------------------------------------------
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Question 2.4. FFTW does not compile on Solaris, complaining about const.
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We know that at least on Solaris 2.5.x with Sun's compilers 4.2 you might
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get error messages from make such as
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"./fftw.h", line 88: warning: const is a keyword in ANSI C
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This is the case when the configure script reports that const does not
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work:
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checking for working const... (cached) no
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You should be aware that Solaris comes with two compilers, namely,
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/opt/SUNWspro/SC4.2/bin/cc and /usr/ucb/cc. The latter compiler is
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non-ANSI. Indeed, it is a perverse shell script that calls the real
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compiler in non-ANSI mode. In order to compile FFTW, change your path so
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that the right cc is used.
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To know whether your compiler is the right one, type cc -V. If the
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compiler prints ``ucbcc'', as in
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ucbcc: WorkShop Compilers 4.2 30 Oct 1996 C 4.2
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then the compiler is wrong. The right message is something like
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cc: WorkShop Compilers 4.2 30 Oct 1996 C 4.2
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-------------------------------------------------------------------------------
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Question 2.5. What's the difference between --enable-3dnow and --enable-k7?
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--enable-k7 enables 3DNow! instructions on K7 processors (AMD Athlon and
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its variants). K7 support is provided by assembly routines generated by a
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special purpose compiler. As of fftw-3.2, --enable-k7 is no longer
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supported.
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--enable-3dnow enables generic 3DNow! support using gcc builtin functions.
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This works on earlier AMD processors, but it is not as fast as our special
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assembly routines. As of fftw-3.1, --enable-3dnow is no longer supported.
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-------------------------------------------------------------------------------
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Question 2.6. What's the difference between the fma and the non-fma versions?
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The fma version tries to exploit the fused multiply-add instructions
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implemented in many processors such as PowerPC, ia-64, and MIPS. The two
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FFTW packages are otherwise identical. In FFTW 3.1, the fma and non-fma
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versions were merged together into a single package, and the configure
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script attempts to automatically guess which version to use.
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The FFTW 3.1 configure script enables fma by default on PowerPC, Itanium,
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and PA-RISC, and disables it otherwise. You can force one or the other by
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using the --enable-fma or --disable-fma flag for configure.
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Definitely use fma if you have a PowerPC-based system with gcc (or IBM
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xlc). This includes all GNU/Linux systems for PowerPC and the older
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PowerPC-based MacOS systems. Also use it on PA-RISC and Itanium with the
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HP/UX compiler.
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Definitely do not use the fma version if you have an ia-32 processor
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(Intel, AMD, MacOS on Intel, etcetera).
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For other architectures/compilers, the situation is not so clear. For
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example, ia-64 has the fma instruction, but gcc-3.2 appears not to exploit
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it correctly. Other compilers may do the right thing, but we have not
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tried them. Please send us your feedback so that we can update this FAQ
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entry.
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-------------------------------------------------------------------------------
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Question 2.7. Which language is FFTW written in?
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FFTW is written in ANSI C. Most of the code, however, was automatically
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generated by a program called genfft, written in the Objective Caml
|
||
|
|
dialect of ML. You do not need to know ML or to have an Objective Caml
|
||
|
|
compiler in order to use FFTW.
|
||
|
|
|
||
|
|
genfft is provided with the FFTW sources, which means that you can play
|
||
|
|
with the code generator if you want. In this case, you need a working
|
||
|
|
Objective Caml system. Objective Caml is available from the Caml web
|
||
|
|
page.
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 2.8. Can I call FFTW from Fortran?
|
||
|
|
|
||
|
|
Yes, FFTW (versions 1.3 and higher) contains a Fortran-callable interface,
|
||
|
|
documented in the FFTW manual.
|
||
|
|
|
||
|
|
By default, FFTW configures its Fortran interface to work with the first
|
||
|
|
compiler it finds, e.g. g77. To configure for a different, incompatible
|
||
|
|
Fortran compiler foobar, use ./configure F77=foobar when installing FFTW.
|
||
|
|
(In the case of g77, however, FFTW 3.x also includes an extra set of
|
||
|
|
Fortran-callable routines with one less underscore at the end of
|
||
|
|
identifiers, which should cover most other Fortran compilers on Linux at
|
||
|
|
least.)
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 2.9. Can I call FFTW from C++?
|
||
|
|
|
||
|
|
Most definitely. FFTW should compile and/or link under any C++ compiler.
|
||
|
|
Moreover, it is likely that the C++ <complex> template class is
|
||
|
|
bit-compatible with FFTW's complex-number format (see the FFTW manual for
|
||
|
|
more details).
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 2.10. Why isn't FFTW written in Fortran/C++?
|
||
|
|
|
||
|
|
Because we don't like those languages, and neither approaches the
|
||
|
|
portability of C.
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 2.11. How do I compile FFTW to run in single precision?
|
||
|
|
|
||
|
|
On a Unix system: configure --enable-float. On a non-Unix system: edit
|
||
|
|
config.h to #define the symbol FFTW_SINGLE (for FFTW 3.x). In both cases,
|
||
|
|
you must then recompile FFTW. In FFTW 3, all FFTW identifiers will then
|
||
|
|
begin with fftwf_ instead of fftw_.
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 2.12. --enable-k7 does not work on x86-64
|
||
|
|
|
||
|
|
Support for --enable-k7 was discontinued in fftw-3.2.
|
||
|
|
|
||
|
|
The fftw-3.1 release supports --enable-k7. This option only works on
|
||
|
|
32-bit x86 machines that implement 3DNow!, including the AMD Athlon and
|
||
|
|
the AMD Opteron in 32-bit mode. --enable-k7 does not work on AMD Opteron
|
||
|
|
in 64-bit mode. Use --enable-sse for x86-64 machines.
|
||
|
|
|
||
|
|
FFTW supports 3DNow! by means of assembly code generated by a
|
||
|
|
special-purpose compiler. It is hard to produce assembly code that works
|
||
|
|
in both 32-bit and 64-bit mode.
|
||
|
|
|
||
|
|
===============================================================================
|
||
|
|
|
||
|
|
Section 3. Using FFTW
|
||
|
|
|
||
|
|
Q3.1 Why not support the FFTW 2 interface in FFTW 3?
|
||
|
|
Q3.2 Why do FFTW 3 plans encapsulate the input/output arrays and not ju
|
||
|
|
Q3.3 FFTW seems really slow.
|
||
|
|
Q3.4 FFTW slows down after repeated calls.
|
||
|
|
Q3.5 An FFTW routine is crashing when I call it.
|
||
|
|
Q3.6 My Fortran program crashes when calling FFTW.
|
||
|
|
Q3.7 FFTW gives results different from my old FFT.
|
||
|
|
Q3.8 FFTW gives different results between runs
|
||
|
|
Q3.9 Can I save FFTW's plans?
|
||
|
|
Q3.10 Why does your inverse transform return a scaled result?
|
||
|
|
Q3.11 How can I make FFTW put the origin (zero frequency) at the center
|
||
|
|
Q3.12 How do I FFT an image/audio file in *foobar* format?
|
||
|
|
Q3.13 My program does not link (on Unix).
|
||
|
|
Q3.14 I included your header, but linking still fails.
|
||
|
|
Q3.15 My program crashes, complaining about stack space.
|
||
|
|
Q3.16 FFTW seems to have a memory leak.
|
||
|
|
Q3.17 The output of FFTW's transform is all zeros.
|
||
|
|
Q3.18 How do I call FFTW from the Microsoft language du jour?
|
||
|
|
Q3.19 Can I compute only a subset of the DFT outputs?
|
||
|
|
Q3.20 Can I use FFTW's routines for in-place and out-of-place matrix tra
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 3.1. Why not support the FFTW 2 interface in FFTW 3?
|
||
|
|
|
||
|
|
FFTW 3 has semantics incompatible with earlier versions: its plans can
|
||
|
|
only be used for a given stride, multiplicity, and other characteristics
|
||
|
|
of the input and output arrays; these stronger semantics are necessary for
|
||
|
|
performance reasons. Thus, it is impossible to efficiently emulate the
|
||
|
|
older interface (whose plans can be used for any transform of the same
|
||
|
|
size). We believe that it should be possible to upgrade most programs
|
||
|
|
without any difficulty, however.
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 3.2. Why do FFTW 3 plans encapsulate the input/output arrays and not just the algorithm?
|
||
|
|
|
||
|
|
There are several reasons:
|
||
|
|
|
||
|
|
* It was important for performance reasons that the plan be specific to
|
||
|
|
array characteristics like the stride (and alignment, for SIMD), and
|
||
|
|
requiring that the user maintain these invariants is error prone.
|
||
|
|
* In most high-performance applications, as far as we can tell, you are
|
||
|
|
usually transforming the same array over and over, so FFTW's semantics
|
||
|
|
should not be a burden.
|
||
|
|
* If you need to transform another array of the same size, creating a new
|
||
|
|
plan once the first exists is a cheap operation.
|
||
|
|
* If you need to transform many arrays of the same size at once, you
|
||
|
|
should really use the plan_many routines in FFTW's "advanced" interface.
|
||
|
|
* If the abovementioned array characteristics are the same, you are
|
||
|
|
willing to pay close attention to the documentation, and you really need
|
||
|
|
to, we provide a "new-array execution" interface to apply a plan to a
|
||
|
|
new array.
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 3.3. FFTW seems really slow.
|
||
|
|
|
||
|
|
You are probably recreating the plan before every transform, rather than
|
||
|
|
creating it once and reusing it for all transforms of the same size. FFTW
|
||
|
|
is designed to be used in the following way:
|
||
|
|
|
||
|
|
* First, you create a plan. This will take several seconds.
|
||
|
|
* Then, you reuse the plan many times to perform FFTs. These are fast.
|
||
|
|
|
||
|
|
If you don't need to compute many transforms and the time for the planner
|
||
|
|
is significant, you have two options. First, you can use the
|
||
|
|
FFTW_ESTIMATE option in the planner, which uses heuristics instead of
|
||
|
|
runtime measurements and produces a good plan in a short time. Second,
|
||
|
|
you can use the wisdom feature to precompute the plan; see Q3.9 `Can I
|
||
|
|
save FFTW's plans?'
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 3.4. FFTW slows down after repeated calls.
|
||
|
|
|
||
|
|
Probably, NaNs or similar are creeping into your data, and the slowdown is
|
||
|
|
due to the resulting floating-point exceptions. For example, be aware
|
||
|
|
that repeatedly FFTing the same array is a diverging process (because FFTW
|
||
|
|
computes the unnormalized transform).
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 3.5. An FFTW routine is crashing when I call it.
|
||
|
|
|
||
|
|
Did the FFTW test programs pass (make check, or cd tests; make bigcheck if
|
||
|
|
you want to be paranoid)? If so, you almost certainly have a bug in your
|
||
|
|
own code. For example, you could be passing invalid arguments (such as
|
||
|
|
wrongly-sized arrays) to FFTW, or you could simply have memory corruption
|
||
|
|
elsewhere in your program that causes random crashes later on. Please
|
||
|
|
don't complain to us unless you can come up with a minimal self-contained
|
||
|
|
program (preferably under 30 lines) that illustrates the problem.
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 3.6. My Fortran program crashes when calling FFTW.
|
||
|
|
|
||
|
|
As described in the manual, on 64-bit machines you must store the plans in
|
||
|
|
variables large enough to hold a pointer, for example integer*8. We
|
||
|
|
recommend using integer*8 on 32-bit machines as well, to simplify porting.
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 3.7. FFTW gives results different from my old FFT.
|
||
|
|
|
||
|
|
People follow many different conventions for the DFT, and you should be
|
||
|
|
sure to know the ones that we use (described in the FFTW manual). In
|
||
|
|
particular, you should be aware that the FFTW_FORWARD/FFTW_BACKWARD
|
||
|
|
directions correspond to signs of -1/+1 in the exponent of the DFT
|
||
|
|
definition. (*Numerical Recipes* uses the opposite convention.)
|
||
|
|
|
||
|
|
You should also know that we compute an unnormalized transform. In
|
||
|
|
contrast, Matlab is an example of program that computes a normalized
|
||
|
|
transform. See Q3.10 `Why does your inverse transform return a scaled
|
||
|
|
result?'.
|
||
|
|
|
||
|
|
Finally, note that floating-point arithmetic is not exact, so different
|
||
|
|
FFT algorithms will give slightly different results (on the order of the
|
||
|
|
numerical accuracy; typically a fractional difference of 1e-15 or so in
|
||
|
|
double precision).
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 3.8. FFTW gives different results between runs
|
||
|
|
|
||
|
|
If you use FFTW_MEASURE or FFTW_PATIENT mode, then the algorithm FFTW
|
||
|
|
employs is not deterministic: it depends on runtime performance
|
||
|
|
measurements. This will cause the results to vary slightly from run to
|
||
|
|
run. However, the differences should be slight, on the order of the
|
||
|
|
floating-point precision, and therefore should have no practical impact on
|
||
|
|
most applications.
|
||
|
|
|
||
|
|
If you use saved plans (wisdom) or FFTW_ESTIMATE mode, however, then the
|
||
|
|
algorithm is deterministic and the results should be identical between
|
||
|
|
runs.
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 3.9. Can I save FFTW's plans?
|
||
|
|
|
||
|
|
Yes. Starting with version 1.2, FFTW provides the wisdom mechanism for
|
||
|
|
saving plans; see the FFTW manual.
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 3.10. Why does your inverse transform return a scaled result?
|
||
|
|
|
||
|
|
Computing the forward transform followed by the backward transform (or
|
||
|
|
vice versa) yields the original array scaled by the size of the array.
|
||
|
|
(For multi-dimensional transforms, the size of the array is the product of
|
||
|
|
the dimensions.) We could, instead, have chosen a normalization that
|
||
|
|
would have returned the unscaled array. Or, to accomodate the many
|
||
|
|
conventions in this matter, the transform routines could have accepted a
|
||
|
|
"scale factor" parameter. We did not do this, however, for two reasons.
|
||
|
|
First, we didn't want to sacrifice performance in the common case where
|
||
|
|
the scale factor is 1. Second, in real applications the FFT is followed or
|
||
|
|
preceded by some computation on the data, into which the scale factor can
|
||
|
|
typically be absorbed at little or no cost.
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 3.11. How can I make FFTW put the origin (zero frequency) at the center of its output?
|
||
|
|
|
||
|
|
For human viewing of a spectrum, it is often convenient to put the origin
|
||
|
|
in frequency space at the center of the output array, rather than in the
|
||
|
|
zero-th element (the default in FFTW). If all of the dimensions of your
|
||
|
|
array are even, you can accomplish this by simply multiplying each element
|
||
|
|
of the input array by (-1)^(i + j + ...), where i, j, etcetera are the
|
||
|
|
indices of the element. (This trick is a general property of the DFT, and
|
||
|
|
is not specific to FFTW.)
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 3.12. How do I FFT an image/audio file in *foobar* format?
|
||
|
|
|
||
|
|
FFTW performs an FFT on an array of floating-point values. You can
|
||
|
|
certainly use it to compute the transform of an image or audio stream, but
|
||
|
|
you are responsible for figuring out your data format and converting it to
|
||
|
|
the form FFTW requires.
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 3.13. My program does not link (on Unix).
|
||
|
|
|
||
|
|
The libraries must be listed in the correct order (-lfftw3 -lm for FFTW
|
||
|
|
3.x) and *after* your program sources/objects. (The general rule is that
|
||
|
|
if *A* uses *B*, then *A* must be listed before *B* in the link command.).
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 3.14. I included your header, but linking still fails.
|
||
|
|
|
||
|
|
You're a C++ programmer, aren't you? You have to compile the FFTW library
|
||
|
|
and link it into your program, not just #include <fftw3.h>. (Yes, this is
|
||
|
|
really a FAQ.)
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 3.15. My program crashes, complaining about stack space.
|
||
|
|
|
||
|
|
You cannot declare large arrays with automatic storage (e.g. via
|
||
|
|
fftw_complex array[N]); you should use fftw_malloc (or equivalent) to
|
||
|
|
allocate the arrays you want to transform if they are larger than a few
|
||
|
|
hundred elements.
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 3.16. FFTW seems to have a memory leak.
|
||
|
|
|
||
|
|
After you create a plan, FFTW caches the information required to quickly
|
||
|
|
recreate the plan. (See Q3.9 `Can I save FFTW's plans?') It also
|
||
|
|
maintains a small amount of other persistent memory. You can deallocate
|
||
|
|
all of FFTW's internally allocated memory, if you wish, by calling
|
||
|
|
fftw_cleanup(), as documented in the manual.
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 3.17. The output of FFTW's transform is all zeros.
|
||
|
|
|
||
|
|
You should initialize your input array *after* creating the plan, unless
|
||
|
|
you use FFTW_ESTIMATE: planning with FFTW_MEASURE or FFTW_PATIENT
|
||
|
|
overwrites the input/output arrays, as described in the manual.
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 3.18. How do I call FFTW from the Microsoft language du jour?
|
||
|
|
|
||
|
|
Please *do not* ask us Windows-specific questions. We do not use Windows.
|
||
|
|
We know nothing about Visual Basic, Visual C++, or .NET. Please find the
|
||
|
|
appropriate Usenet discussion group and ask your question there. See also
|
||
|
|
Q2.2 `Does FFTW run on Windows?'.
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 3.19. Can I compute only a subset of the DFT outputs?
|
||
|
|
|
||
|
|
In general, no, an FFT intrinsically computes all outputs from all inputs.
|
||
|
|
In principle, there is something called a *pruned FFT* that can do what
|
||
|
|
you want, but to compute K outputs out of N the complexity is in general
|
||
|
|
O(N log K) instead of O(N log N), thus saving only a small additive factor
|
||
|
|
in the log. (The same argument holds if you instead have only K nonzero
|
||
|
|
inputs.)
|
||
|
|
|
||
|
|
There are some specific cases in which you can get the O(N log K)
|
||
|
|
performance benefits easily, however, by combining a few ordinary FFTs.
|
||
|
|
In particular, the case where you want the first K outputs, where K
|
||
|
|
divides N, can be handled by performing N/K transforms of size K and then
|
||
|
|
summing the outputs multiplied by appropriate phase factors. For more
|
||
|
|
details, see pruned FFTs with FFTW.
|
||
|
|
|
||
|
|
There are also some algorithms that compute pruned transforms
|
||
|
|
*approximately*, but they are beyond the scope of this FAQ.
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 3.20. Can I use FFTW's routines for in-place and out-of-place matrix transposition?
|
||
|
|
|
||
|
|
You can use the FFTW guru interface to create a rank-0 transform of vector
|
||
|
|
rank 2 where the vector strides are transposed. (A rank-0 transform is
|
||
|
|
equivalent to a 1D transform of size 1, which. just copies the input into
|
||
|
|
the output.) Specifying the same location for the input and output makes
|
||
|
|
the transpose in-place.
|
||
|
|
|
||
|
|
For double-valued data stored in row-major format, plan creation looks
|
||
|
|
like this:
|
||
|
|
|
||
|
|
fftw_plan plan_transpose(int rows, int cols, double *in, double *out)
|
||
|
|
{
|
||
|
|
const unsigned flags = FFTW_ESTIMATE; /* other flags are possible */
|
||
|
|
fftw_iodim howmany_dims[2];
|
||
|
|
|
||
|
|
howmany_dims[0].n = rows;
|
||
|
|
howmany_dims[0].is = cols;
|
||
|
|
howmany_dims[0].os = 1;
|
||
|
|
|
||
|
|
howmany_dims[1].n = cols;
|
||
|
|
howmany_dims[1].is = 1;
|
||
|
|
howmany_dims[1].os = rows;
|
||
|
|
|
||
|
|
return fftw_plan_guru_r2r(/*rank=*/ 0, /*dims=*/ NULL,
|
||
|
|
/*howmany_rank=*/ 2, howmany_dims,
|
||
|
|
in, out, /*kind=*/ NULL, flags);
|
||
|
|
}
|
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|
|
(This entry was written by Rhys Ulerich.)
|
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|
|
|
||
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|
===============================================================================
|
||
|
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||
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|
Section 4. Internals of FFTW
|
||
|
|
|
||
|
|
Q4.1 How does FFTW work?
|
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|
|
Q4.2 Why is FFTW so fast?
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 4.1. How does FFTW work?
|
||
|
|
|
||
|
|
The innovation (if it can be so called) in FFTW consists in having a
|
||
|
|
variety of composable *solvers*, representing different FFT algorithms and
|
||
|
|
implementation strategies, whose combination into a particular *plan* for
|
||
|
|
a given size can be determined at runtime according to the characteristics
|
||
|
|
of your machine/compiler. This peculiar software architecture allows FFTW
|
||
|
|
to adapt itself to almost any machine.
|
||
|
|
|
||
|
|
For more details (albeit somewhat outdated), see the paper "FFTW: An
|
||
|
|
Adaptive Software Architecture for the FFT", by M. Frigo and S. G.
|
||
|
|
Johnson, *Proc. ICASSP* 3, 1381 (1998), also available at the FFTW web
|
||
|
|
page.
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 4.2. Why is FFTW so fast?
|
||
|
|
|
||
|
|
This is a complex question, and there is no simple answer. In fact, the
|
||
|
|
authors do not fully know the answer, either. In addition to many small
|
||
|
|
performance hacks throughout FFTW, there are three general reasons for
|
||
|
|
FFTW's speed.
|
||
|
|
|
||
|
|
* FFTW uses a variety of FFT algorithms and implementation styles that
|
||
|
|
can be arbitrarily composed to adapt itself to a machine. See Q4.1 `How
|
||
|
|
does FFTW work?'.
|
||
|
|
* FFTW uses a code generator to produce highly-optimized routines for
|
||
|
|
computing small transforms.
|
||
|
|
* FFTW uses explicit divide-and-conquer to take advantage of the memory
|
||
|
|
hierarchy.
|
||
|
|
|
||
|
|
For more details (albeit somewhat outdated), see the paper "FFTW: An
|
||
|
|
Adaptive Software Architecture for the FFT", by M. Frigo and S. G.
|
||
|
|
Johnson, *Proc. ICASSP* 3, 1381 (1998), available along with other
|
||
|
|
references at the FFTW web page.
|
||
|
|
|
||
|
|
===============================================================================
|
||
|
|
|
||
|
|
Section 5. Known bugs
|
||
|
|
|
||
|
|
Q5.1 FFTW 1.1 crashes in rfftwnd on Linux.
|
||
|
|
Q5.2 The MPI transforms in FFTW 1.2 give incorrect results/leak memory.
|
||
|
|
Q5.3 The test programs in FFTW 1.2.1 fail when I change FFTW to use sin
|
||
|
|
Q5.4 The test program in FFTW 1.2.1 fails for n > 46340.
|
||
|
|
Q5.5 The threaded code fails on Linux Redhat 5.0
|
||
|
|
Q5.6 FFTW 2.0's rfftwnd fails for rank > 1 transforms with a final dime
|
||
|
|
Q5.7 FFTW 2.0's complex transforms give the wrong results with prime fa
|
||
|
|
Q5.8 FFTW 2.1.1's MPI test programs crash with MPICH.
|
||
|
|
Q5.9 FFTW 2.1.2's multi-threaded transforms don't work on AIX.
|
||
|
|
Q5.10 FFTW 2.1.2's complex transforms give incorrect results for large p
|
||
|
|
Q5.11 FFTW 2.1.3's multi-threaded transforms don't give any speedup on S
|
||
|
|
Q5.12 FFTW 2.1.3 crashes on AIX.
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 5.1. FFTW 1.1 crashes in rfftwnd on Linux.
|
||
|
|
|
||
|
|
This bug was fixed in FFTW 1.2. There was a bug in rfftwnd causing an
|
||
|
|
incorrect amount of memory to be allocated. The bug showed up in Linux
|
||
|
|
with libc-5.3.12 (and nowhere else that we know of).
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 5.2. The MPI transforms in FFTW 1.2 give incorrect results/leak memory.
|
||
|
|
|
||
|
|
These bugs were corrected in FFTW 1.2.1. The MPI transforms (really, just
|
||
|
|
the transpose routines) in FFTW 1.2 had bugs that could cause errors in
|
||
|
|
some situations.
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 5.3. The test programs in FFTW 1.2.1 fail when I change FFTW to use single precision.
|
||
|
|
|
||
|
|
This bug was fixed in FFTW 1.3. (Older versions of FFTW did work in
|
||
|
|
single precision, but the test programs didn't--the error tolerances in
|
||
|
|
the tests were set for double precision.)
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 5.4. The test program in FFTW 1.2.1 fails for n > 46340.
|
||
|
|
|
||
|
|
This bug was fixed in FFTW 1.3. FFTW 1.2.1 produced the right answer, but
|
||
|
|
the test program was wrong. For large n, n*n in the naive transform that
|
||
|
|
we used for comparison overflows 32 bit integer precision, breaking the
|
||
|
|
test.
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 5.5. The threaded code fails on Linux Redhat 5.0
|
||
|
|
|
||
|
|
We had problems with glibc-2.0.5. The code should work with glibc-2.0.7.
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 5.6. FFTW 2.0's rfftwnd fails for rank > 1 transforms with a final dimension >= 65536.
|
||
|
|
|
||
|
|
This bug was fixed in FFTW 2.0.1. (There was a 32-bit integer overflow
|
||
|
|
due to a poorly-parenthesized expression.)
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 5.7. FFTW 2.0's complex transforms give the wrong results with prime factors 17 to 97.
|
||
|
|
|
||
|
|
There was a bug in the complex transforms that could cause incorrect
|
||
|
|
results under (hopefully rare) circumstances for lengths with
|
||
|
|
intermediate-size prime factors (17-97). This bug was fixed in FFTW
|
||
|
|
2.1.1.
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 5.8. FFTW 2.1.1's MPI test programs crash with MPICH.
|
||
|
|
|
||
|
|
This bug was fixed in FFTW 2.1.2. The 2.1/2.1.1 MPI test programs crashed
|
||
|
|
when using the MPICH implementation of MPI with the ch_p4 device (TCP/IP);
|
||
|
|
the transforms themselves worked fine.
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 5.9. FFTW 2.1.2's multi-threaded transforms don't work on AIX.
|
||
|
|
|
||
|
|
This bug was fixed in FFTW 2.1.3. The multi-threaded transforms in
|
||
|
|
previous versions didn't work with AIX's pthreads implementation, which
|
||
|
|
idiosyncratically creates threads in detached (non-joinable) mode by
|
||
|
|
default.
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 5.10. FFTW 2.1.2's complex transforms give incorrect results for large prime sizes.
|
||
|
|
|
||
|
|
This bug was fixed in FFTW 2.1.3. FFTW's complex-transform algorithm for
|
||
|
|
prime sizes (in versions 2.0 to 2.1.2) had an integer overflow problem
|
||
|
|
that caused incorrect results for many primes greater than 32768 (on
|
||
|
|
32-bit machines). (Sizes without large prime factors are not affected.)
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 5.11. FFTW 2.1.3's multi-threaded transforms don't give any speedup on Solaris.
|
||
|
|
|
||
|
|
This bug was fixed in FFTW 2.1.4. (By default, Solaris creates threads
|
||
|
|
that do not parallelize over multiple processors, so one has to request
|
||
|
|
the proper behavior specifically.)
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Question 5.12. FFTW 2.1.3 crashes on AIX.
|
||
|
|
|
||
|
|
The FFTW 2.1.3 configure script picked incorrect compiler flags for the
|
||
|
|
xlc compiler on newer IBM processors. This is fixed in FFTW 2.1.4.
|
||
|
|
|